Question

a 49 - foot piece of siding is cut into three pieces so that the second piece is twice as long as the first piece and the third piece is four times as long as the first piece. if x represents the length of the first piece, find the lengths of all three pieces. the length of the first piece of siding is ft long, the length of the second piece is ft long, and the length of the third piece is ft long.

Explanation:

Step1: Set up an equation

Let the length of the first - piece be $x$ feet. Then the second piece is $2x$ feet and the third piece is $4x$ feet. The sum of the lengths of the three pieces is equal to the total length of the siding, so $x + 2x+4x=49$.

Step2: Combine like - terms

Combining the left - hand side of the equation, we get $7x = 49$.

Step3: Solve for $x$

Dividing both sides of the equation $7x = 49$ by 7, we have $x=\frac{49}{7}=7$.

Step4: Find the lengths of the other pieces

The second piece: $2x = 2\times7 = 14$ feet.
The third piece: $4x = 4\times7 = 28$ feet.

Answer:

The length of the first piece is 7 ft, the length of the second piece is 14 ft, and the length of the third piece is 28 ft.